3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the interval [0,1]

Q: Find the area of the surface x2 - 2 ln x + sqrt(15)y - z = 0 above the square R: 1<=x <= 2,…

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Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

Q: Find the area of the surface generated by revolving the semicircle y = √1 − x about the x-axis over…

A: Given that, y=1-x. dydx=121-x-12·-1=-121-x 1+dydx2=1+-121-x2=1+141-x=1+14-4x=4-4x+14-4x=5-4x4-4x

Q: Find the area of the surface formed by revolving the graph of f (x) = x2 on the interval [0,√2]…

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Q: Let S be the shape obtained by rotating f(x) = 2 /x +1 on the interval [1, 3] around the x-axis.…

A: Given :fx = 2x+1

Q: Find the area between the curve y = cos (2x) and the line joining the points (pi/4, 0) and (pi/6,…

A: Area of the region is (2-√3)/4

Q: Solve the area covered by the x-axis and f(x) = e^x from x= 1 to x = 4 with interval h = 0.25 using:…

A: ∫abf(x)dx≈Δx(f(x0+x12)+f(x1+x22)+f(x2+x32)+⋯+f(xn−2+xn−12)+f(xn−1+xn2)) Mid point rule and…

Q: 5. Find the area of the surface obtained by rotating the curve about the x-axis: x' + 6. 1 <x<1 1 2x

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Q: Find the surface area of revolution about the y-axis of y=6x+3 over the interval 0 ≤ x ≤ 3

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Q: 7) (g) Set up and evaluate the definite integral for the area of the surface generated by revolving…

A: we use integration formula for area of surface rotating about x-axis..

Q: 9. (a) Calculate the area of the region bounded by the curves y = x² +1 and y = xª between x = 0 and…

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Q: 4- Find the area of the region bounded by the curves y - 3x = 4 and 3r – 2y = 11. a) b) e) d) e)

A: The equation of the curves are : C1 :  y2-3x = 4  ⇒ x = y2-43 C2 : 3x-2y = 11  ⇒ x = 2y+113 To…

Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 0≤x≤1

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Q: Find the surface area of revolution about the x-axis of y 4x +7 over the interval 0 < r<3

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Q: d the area of the region bounded by the curves: y = cos(nx) and y = -1 + 4x²

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Q: 2. Find the total area of the region between the curves y = sinx and y = cosx for 0<xs 37 2

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Q: Find the area of the surface formed by revolving the graph of f (x) = x³ on the interval [0,1]…

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Q: Find the surface area of revolution about the x-axis of y = 3 sin(6x) over the interval 0 <x < -

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Q: 7) Set up and evaluate the definite integral for the area of the surface generated by revolving y…

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Q: Find the area of the region bounded by the curve x³ x² + 2xy - y² = 0 and the line x = 4. (HINT:…

A: Given  x3 x2 + 2xy - y2 =0 x3 = (y - x )2 x3/2x = y      and   y = -x3/2x   AREA = ∫x1x21f(x)-g(x)dx…

Q: Find the surface area of revolution about the x-axis of y = 7 sin(3x) over the interval 0 < x <

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Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: 2. Find the surface area when y = 2\x with 1 < x < 3 is rotated around the x axis.

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Q: 3. Find the surface area generated by rotating y=- bounded by y=0_ x=0 , and x=9 about the the…

A: Surface area generated by rotating a curve y = f(x) about the x-axis from x = a to x = b is given by…

Q: Find the surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: Calculate the surface area of revolution of f(x) = 3√(x) + 2 about the y-axis in [2,8]. Graph.

A: Given data:   The expression for the given function is: f(x)=x1/3+2.   The expression for the given…

Q: f(x) = }x* + [1, V2]

A:

Q: 7 Find the area of the surface generated by revolving x = 2/4-y, 0sys about the y-axis.

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Q: Find the surface area of revolution about the x-axis of 6x +1 over the interval 2 < z < 3

A: Given y=6x+1 over the interval 2≤x≤3

Q: Find the area of the surface formed by revolving the graph of y = Vx + 2 on the interval [1,8] about…

A:

Q: 3. Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis…

A: Follow the procedure given below.

Q: Find the surface area of revolution about the x-axis of y = 3x + 2 over the interval 0 < z <1

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Q: 7) Find the area of the surface that is formed by revolving the function y = 2 x on the interval %3D…

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Q: 2. Find the area of the surface obtained by revolving the curve g(x) = Vx +1 on the interval 0 < x <…

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Q: Find the surface area of revolution about the x-axis of y 7x + 7 over the interval 0 < a < 3

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Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

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Q: Find the surface area of revolution about the x-axis of y = 4 sin(4x) over the interval 0 < x < 4

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Q: Q1) Find the areas of the regions enclose y = 8 cos x and y = sec2 x, -<

A: Lets find the intersection of the graphs of the function y=8 cos x and y= sec2 x on the interval…

Q: 8. Find the area of the surface of the region generated by rotating the curve y = x³ from x=0 to x=1…

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Q: 6. Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: 4. Find the surface area of the function x when revolved around the x-axis. between x=0 and x1

A: When a curve is revolved about an axis, we obtain a surface and there are several pre-defined…

Q: Find the surface area of revolution about the y-axis of y = 5x + 1 over the interval 0 < x < 3

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Q: Find the surface area of revolution about the x-axis of y = 2x + 6 over the interval 2 < x < 5

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x.

A: Given: y=e-9x and 0, 1 To find the surface of revolution about the x-axis on 0, 1 The formula for…

Q: Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis from…

A: Given: fx=sinx0≤x≤π2 It is required to find the area of surface of the curve when it is revolved…

Q: Find the area of the region bounded by the two curves: y = sin 2r, y = tan r, for z 20, and r< 2.

A: Here, y=sin(2x) , y=tanx , 0≤x&lt;π2 Region bounded by these two curves in the interval 0≤x&lt;π2 is…

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

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Q: Find the surface area of revolution about the x-axis of y = 6 sin(7x) over the interval 0 < x < 7

A: Here we have y=6sin(7x)  We have to find surface area of revolution about x axis in interval 0 to…